Letter pubs.acs.org/NanoLett
Probing Electronic Excitations in Mono- to Pentalayer Graphene by Micro Magneto-Raman Spectroscopy Stéphane Berciaud,*,† Marek Potemski,‡ and Clément Faugeras*,‡ †
Institut de Physique et Chimie des Matériaux de Strasbourg and NIE, UMR 7504, Université de Strasbourg and CNRS, 23 rue du Lœss, BP43, 67034 Strasbourg Cedex 2, France ‡ Laboratoire National des Champs Magnétiques Intenses, CNRS/UJF/UPS/INSA, Grenoble F-38042, France S Supporting Information *
ABSTRACT: We probe electronic excitations between Landau levels in freestanding N-layer graphene over a broad energy range, with unprecedented spectral and spatial resolution, using micro magneto-Raman scattering spectroscopy. A characteristic evolution of electronic bands in up to five Bernal-stacked graphene layers is evidenced and shown to remarkably follow a simple theoretical approach, based on an effective bilayer model. (N > 3)-layer graphenes appear as appealing candidates in the quest for novel phenomena, particularly in the quantum Hall effect regime. Our work paves the way toward minimally invasive investigations of magneto-excitons in other emerging low-dimensional systems, with a spatial resolution down to 1 μm. KEYWORDS: Freestanding graphene, magneto-Raman scattering, electronic excitations, Landau levels, effective bilayer
S
submicrometer spatial resolution, characteristic of visible-light techniques. Indeed, Raman scattering spectroscopy has been widely used to study the electronic excitations in solids and particularly in semiconductors, including two-dimensional electron gases in the quantum Hall effect regime.19 So far, however, these studies have been limited to probing electronic excitations in the vicinity of the Fermi energy (intraband excitations, in case of QHE systems). In contrast, the electronic Raman scattering response of graphitic materials is much richer. It may involve both intraband and interband (across the neutrality point) contributions, as theoretically predicted20,21 and observed in experiments, e.g., on graphite,22,23 graphene on graphite,24 and carbon nanotubes.25 Here, employing MMRSS, with transverse magnetic fields B up to 29 T, we were able to directly trace the electronic Raman scattering features associated with symmetric inter Landau levels transitions in freestanding N-LG, from mono- to pentalayer graphene. The dispersion of these excitations with the magnetic field is a hallmark of the number of layers and permits a precise determination of electronic dispersions. With
earching for materials with new functionalities and deepening our knowledge on already identified structures are primary directions in the research on novel two-dimensional systems, which include the family of Bernal-stacked N-layer graphene. Each member of this family displays very distinct electronic properties. This is expected from theory1−4 and confirmed in experiments on graphene and its bilayer, especially when profiting from a conversion of two-dimensional electronic bands into quantum Hall effect (QHE) systems with characteristically spaced-in-energy Landau levels.5−10 Of prime interest are high-quality specimens, often fragile and of small lateral size, thus calling for adequate experimental probes. A well-established path toward obtaining intrinsically pure graphene consists in isolating freestanding layers.11−13 Such high quality comes at the cost of the relatively small area (typically 2, the magnetoRaman spectra then become increasingly rich. To clearly visualize electronic excitations, we now consider the contour plot built from the magneto-Raman spectra recorded as a function of B (see Figure 3) on a diffraction limited spot. On these maps, the dispersion of the electronic Raman features identified in Figure 2 appear prominently. The difference between the dispersion of the ERS features in monoand bilayer graphene is particularly striking. The high sensitivity of our setup allows us to trace up to 2, 3, 5, 7, and 9 excitations in N = 1 to N = 5 layer graphene, respectively. As anticipated theoretically, monolayer-like dispersions are only observed for odd N, while bilayer-like dispersions appear for N > 1. Figure 3e−i shows the extracted frequency of all the observable ERS features, along with fits, based on the model described above for the corresponding N. Interestingly, the LL dispersions observed in freestanding monolayer graphene deviate significantly from the expected (nB)1/2 scaling and suggest average Fermi velocities of ∼1.3 × 106 m/s, significantly larger than the values of ∼1.0−1.1 × 106 m/s from previous magneto-absorption studies on supported graphene.18 First, the relatively high values of vF observed in monolayer graphene likely stem from the reduction of dielectric screening in freestanding graphene.33,34 Second, the peculiar scaling of Lπ/2 −n,n with n and B observed for N = 1 (see Figure 3a,f) is presumably a consequence of many body Coulomb interactions in freestanding graphene. For example, recent electron transport measurements on freestanding graphene devices have revealed a logarithmic divergence of the Fermi velocity in the close vicinity of the Dirac point.33 This behavior has been assigned to electron−electron interactions. In our work, from the Raman scattering spectrum measured at B = 0 T, we estimate a residual doping below ∼2 × 1011 cm−2,13,31 a value at which such interaction effects become significant.33 A comprehensive analysis of the influence of many-body effects on the magneto excitons in freestanding graphene and, subsequently, on the evolution of the Fermi velocity in the presence of a magnetic field,35 goes beyond the scope of the present study and will be discussed elsewhere. In comparison, for N = 2 to N = 5, the dispersions of all the observed ERS features resemble the theoretical patterns introduced in Figure 1 and are quantitatively reproduced by the effective bilayer model. At a given value of θ, we observe that the Lθ−n,n transition exhibits a steeper dispersion as a function of B for smaller N. Within the effective bilayer framework, and using a fixed value of γ1 = 400 meV, in keeping with previous measurements on bulk graphite,18,26 this translates into a slight reduction of the Fermi velocity from vF = (1.09 ± 0.01) × 106 m/s for N = 2 down to (1.05 ± 0.01) × 106 m/s for N = 5. We have also attempted to fit our results using the values of Lθ−n,n derived from the Slonczewski−Weiss− McClure model for the dispersion of bulk graphite.36 Using several additional fitting parameters, this model provides a marginally better fit to our data and also suggests a very similar reduction of vF with increasing N. Our observations also suggest
that for N > 1, the existence of low-energy, gapless electronic bands with finite curvature, and the subsequent finite density of states at the Dirac point at B = 0 T and increased degeneracy of the n = 0 LL at finite B, play an essential role in defining the Fermi velocity. Altogether, the apparent decrease of vF with increasing N is consistent with the value of vF = 1.02 × 106 m/s observed in bulk graphite26 and with recent angle resolved photoemission spectroscopy measurements on graphene monolayers deposited on various substrates.34 In conclusion, our results demonstrate the richness of the electronic excitation spectra in N-layer graphene and reveals a peculiar dispersion of Landau levels in monolayer graphene, thus opening interesting avenues for the study of many-body effects on its magneto-optical conductivity. The experimental methodology presented here permits the optical probing of electron−hole quasiparticles, from energies as low as ∼100 meV in monolayer graphene, and down to ∼60 meV in (N > 1)-layer graphene, using moderate magnetic fields of a few T. In addition, most of the electronic excitations presented in this work can readily be observed using magnetic fields below 12 T, accessible with commercially available superconducting magnets. Consequently, table-top micro magneto Raman scattering experiments, may be developed to unravel electronic excitations in the close vicinity of the charge neutrality point of N-layer graphene and to further investigate the electronic dispersion of these systems. Finally, our work provides an impetus for studies of (N > 3)-layer graphene in the Quantum Hall effect regime,4 in which new broken symmetry states37 can be expected due to extra crossings of Landau level and/or Landau level bunching over a broad range of magnetic field. We also believe that further improvement of the experimental arrangements will allow us to measure the excitations in a close vicinity to the laser line, thus offering an optical probe of small energy gaps, such as, for example, those arising from lifting the spin or valley degeneracy.38
■
ASSOCIATED CONTENT
S Supporting Information *
Spatially resolved, low temperature micro-Raman characterization of a freestanding graphene monolayer at zero magnetic field, comparison between the magneto-Raman scattering spectra of freestanding and supported samples, false-color maps of the differentiated micro-Raman scattering spectra of mono- to pentalayer graphene as a function of the magnetic field. This material is available free of charge via the Internet at http://pubs.acs.org.
■
AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS We are grateful to M. Orlita, P. Kossacki, and D.M Basko for numerous discussions. We also thank Ivan Breslavetz for technical support and R. Bernard, S. Siegwald, and H. Majjad for help with sample preparation in the StNano clean room facility. S.B. acknowledges support from the Agence nationale de la recherche (under grant QuanDoGra 12 JS10-001-01), from the CNRS and Université de Strasbourg and from the 4552
dx.doi.org/10.1021/nl501578m | Nano Lett. 2014, 14, 4548−4553
Nano Letters
Letter
(30) Faugeras, C.; Amado, M.; Kossacki, P.; Orlita, M.; Sprinkle, M.; Berger, C.; de Heer, W. A.; Potemski, M. Phys. Rev. Lett. 2009, 103, 186803. (31) Berciaud, S.; Li, X.; Htoon, H.; Brus, L. E.; Doorn, S. K.; Heinz, T. F. Nano Lett. 2013, 13, 3517−3523. (32) Ferrari, A. C.; Basko, D. M. Nat. Nanotechnol. 2013, 8, 235−246. (33) Elias, D. C.; Gorbachev, R. V.; Mayorov, A. S.; Morozov, S. V.; Zhukov, A. A.; Blake, P.; Ponomarenko, L. A.; Grigorieva, I. V.; Novoselov, K. S.; Guinea, F.; Geim, A. K. Nat. Phys. 2011, 7, 701−704. (34) Hwang, C.; Siegel, D.; Mo, S.-K.; Regan, W.; Ismach, A.; Zhang, Y.; Zettl, A.; Lanzara, A. Sci. Rep. 2012, 2, 590. (35) Shizuya, K. Phys. Rev. B 2011, 84, 075409. (36) Nakao, K. J. Phys. Soc. Jpn. 1976, 40, 761−768. (37) Taychatanapat, T.; Watanabe, K.; Taniguchi, T.; Jarillo-Herrero, P. Nat. Phys. 2011, 7, 621−625. (38) Feldman, B. E.; Martin, J.; Yacoby, A. Nat. Phys. 2009, 5, 889− 893.
LNCMI-CNRS, member of the European Magnetic Field Laboratory (EMFL). M.P. and C.F. acknowledge support from the ERC-2012-AdG-320590 MOMB project and the EC graphene flagship.
■
REFERENCES
(1) Latil, S.; Henrard, L. Phys. Rev. Lett. 2006, 97, 036803. (2) Partoens, B.; Peeters, F. M. Phys. Rev. B 2007, 75, 193402. (3) Koshino, M.; Ando, T. Phys. Rev. B 2007, 76, 085425. (4) Koshino, M.; McCann, E. Phys. Rev. B 2011, 83, 165443. (5) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Nature 2005, 438, 197−200. (6) Zhang, Y.; Tan, Y.-W.; Stormer, H. L.; Kim, P. Nature 2005, 438, 201−204. (7) Novoselov, K. S.; McCann, E.; Morozov, S. V.; Fal’ko, V. I.; Katsnelson, M. I.; Zeitler, U.; Jiang, D.; Schedin, F.; Geim, A. K. Nat. Phys. 2006, 2, 177−180. (8) Sadowski, M.; Martinez, G.; Potemski, M.; Berger, C.; de Heer, W. A. Phys. Rev. Lett. 2006, 97, 266405. (9) Jiang, Z.; Henriksen, E. A.; Tung, L. C.; Wang, Y.-J.; Schwartz, M. E.; Han, M. Y.; Kim, P.; Stormer, H. L. Phys. Rev. Lett. 2007, 98, 197403. (10) Henriksen, E. A.; Jiang, Z.; Tung, L.-C.; Schwartz, M. E.; Takita, M.; Wang, Y.-J.; Kim, P.; Stormer, H. L. Phys. Rev. Lett. 2008, 100, 087403. (11) Bolotin, K. I.; Sikes, K. J.; Jiang, Z.; Klima, M.; Fudenberg, G.; Hone, J.; Kim, P.; Stormer, H. L. Solid State Commun. 2008, 146, 351− 355. (12) Du, X.; Skachko, I.; Duerr, F.; Luican, A.; Andrei, E. Y. Nature 2009, 462, 192−195. (13) Berciaud, S.; Ryu, S.; Brus, L. E.; Heinz, T. F. Nano Lett. 2009, 9, 346. (14) Ohta, T.; Bostwick, A.; McChesney, J. L.; Seyller, T.; Horn, K.; Rotenberg, E. Phys. Rev. Lett. 2007, 98, 206802. (15) Coletti, C.; Forti, S.; Principi, A.; Emtsev, K. V.; Zakharov, A. A.; Daniels, K. M.; Daas, B. K.; Chandrashekhar, M. V. S.; Ouisse, T.; Chaussende, D.; MacDonald, A. H.; Polini, M.; Starke, U. Phys. Rev. B 2013, 88, 155439. (16) Li, G.; Luican, A.; Andrei, E. Y. Phys. Rev. Lett. 2009, 102, 176804. (17) Mak, K. F.; Sfeir, M. Y.; Misewich, J. A.; Heinz, T. F. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 14999. (18) Orlita, M.; Potemski, M. Semiconductor Sci. Technol. 2010, 25, 063001. (19) Pinczuk, A. In Perspectives in Quantum Hall Effect; Das Sarma, S., Pinczuk, A., Eds.; John Wiley & Sons, Inc.: New York, 1997; p 307. (20) Kashuba, O.; Fal’ko, V. I. Phys. Rev. B 2009, 80, 241404. (21) Mucha-Kruczyński, M.; Kashuba, O.; Fal’ko, V. I. Phys. Rev. B 2010, 82, 045405. (22) Kossacki, P.; Faugeras, C.; Kühne, M.; Orlita, M.; Nicolet, A. A. L.; Schneider, J. M.; Basko, D. M.; Latyshev, Y. I.; Potemski, M. Phys. Bev. B 2011, 84, 235138. (23) Ma, Y.; Kim, Y.; Kalugin, N. G.; Lombardo, A.; Ferrari, A. C.; Kono, J.; Imambekov, A.; Smirnov, D. Phys. Rev. B 2014, 89, 121402. (24) Faugeras, C.; Amado, M.; Kossacki, P.; Orlita, M.; Kühne, M.; Nicolet, A. A. L.; Latyshev, Y. I.; Potemski, M. Phys. Rev. Lett. 2011, 107, 036807. (25) Farhat, H.; Berciaud, S.; Kalbac, M.; Saito, R.; Heinz, T. F.; Dresselhaus, M. S.; Kong, J. Phys. Rev. Lett. 2011, 107, 157401. (26) Orlita, M.; Faugeras, C.; Schneider, J. M.; Martinez, G.; Maude, D. K.; Potemski, M. Phys. Rev. Lett. 2009, 102, 166401. (27) McCann, E.; Fal’ko, V. I. Phys. Rev. Lett. 2006, 96, 086805. (28) Ando, T. J. Phys. Soc. Jpn. 2007, 76, 024712. (29) Goerbig, M. O.; Fuchs, J.-N.; Kechedzhi, K.; Fal’ko, V. I. Phys. Rev. Lett. 2007, 99, 087402. Goerbig, M. O.; Fuchs, J.-N.; Kechedzhi, K.; Fal’ko, V. I. Erratum: ibid. 2009, 103 (17), 179901. 4553
dx.doi.org/10.1021/nl501578m | Nano Lett. 2014, 14, 4548−4553
